Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay
Joint Authors
Tang, Sanyi
Qi, Junmei
Shi, Ruiqing
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-25
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We propose a two-dimensional predatory-prey model with discrete and distributed delay.
By the use of a new variable, the original two-dimensional system transforms into an equivalent three-dimensional system.
Firstly, we study the existence and local stability of equilibria of the new system.
And, by choosing the time delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the time delay τ passes through some critical values.
Secondly, by the use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation.
At last, an example with numerical simulations is provided to verify the theoretical results.
In addition, some simple discussion is also presented.
American Psychological Association (APA)
Shi, Ruiqing& Qi, Junmei& Tang, Sanyi. 2013. Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-472848
Modern Language Association (MLA)
Shi, Ruiqing…[et al.]. Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-472848
American Medical Association (AMA)
Shi, Ruiqing& Qi, Junmei& Tang, Sanyi. Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-472848
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-472848